Subgroups — C₂²⋊(C₅²⋊C₃) #64500

Order 300.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²⋊C₃	—	4	1	no	maximal, Hall
3	C₂×C₅²	—	3	1	no	—
4	C₅²	A₄	1	1	yes	characteristic, complemented, Sylow
5	C₂²×C₅	—	3	2	no	—
6	A₄	—	25	1	no	maximal, Hall
7	C₂×C₅	—	3	6	no	—
8	C₅	—	3	2	no	—
9	C₂²	C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
10	C₃	—	100	1	no	Sylow
11	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₅²	C₃
LCS	G ▷ C₂²×C₅²
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.